Rick Santorum has admitted authorising "robocalls" to encourage Democrats to participate in the Michigan Republican primary and to vote against rival Mitt Romney.

Romney had accused him of resorting to dirty tricks on the eve of Tuesday's primary. Speaking to Fox News, Romney said Santorum's tactic of automated phone calls to registered Democrats, which is legitimate but could be regarded as underhand, marked a new low in the campaign.

"Senator Santorum did something today which I think is deceptive and a dirty trick," Romney said.

An influx of Democratic votes could make the difference in a tight contest. Polls show Romney and Santorum neck-and-neck, with Santorum enjoying a late surge.

After the long slog of primaries and caucuses since Iowa on 3 January, Michigan could prove make or break for both campaigns, with Romney either confirming his frontrunner status or handing it over to Santorum before next week's Super Tuesday contests, when 10 states hold elections to choose delegates who go on to nominate the presidential candidate.

Although the Michigan primary is a Republican one, America's quirky election system allows Democrats and independents to turn up at polling booths, declare themselves to be temporarily Republicans and to vote. In other states where there are similar open contests, Democrats tend not to abuse the system.

But Democratic activists in Michigan have been encouraging Democrats to vote in the Republican race against Romney, a piece of mischief aimed at throwing the Republican presidential process into disarray.

But in an unusual move, Santorum has backed the Democrats' campaign with a robocall seeking to exploit Romney's opposition to the federal bailout of the car industry in 2008. The robocall, revealed by Talking

Points Memo, says: "Michigan Democrats can vote in the Republican primary on Tuesday. Why is it so important? Romney supported the bailout for his Wall Street billionaire buddies, but opposed the auto bailout. That was a slap in the face to every Michigan worker. And we're not going to let Romney get away with it." The narrator adds that the robocall is authorised by Santorum.

The Santorum campaign later confirmed that it was behind the robocalls, and the candidate defended the tactic, arguing that attracting Democrats is a necessary part of winning a White House election.

If Romney loses, he can claim that Santorum won with the support of Democrats.

Santorum was in the lead in Michigan two weeks ago. That lead evaporated, leaving the two tied, but Santorum has been gaining the bigger crowds on the campaign trail and that is being reflected in a late surge in the polls.

At a rally in Kalamazoo on Monday night, he filled a hall to its capacity of 400. An overflow room took another 150 and the organisers claimed a further 400 were turned away.

Santorum told the crowd: "I think we are going to surprise a few people tomorrow night."

Romney's campaign has repeatedly misfired, with mistakes such as choosing as a campaign venue a near-empty football stadium in Detroit on Friday.

At the same event he reinforced his image as the mega-rich candidate out of touch with the average American by casually mentioning his wife had two luxury Cadillacs.

His campaign team were still addressing the issue on Monday, saying the Cadillacs quote would not resonate in Michigan as it was the centre of US car manufacturing.

Romney made a similar gaffe on Sunday. He briefly left the campaign trail in Michigan to put in an appearance at a Nascar racing event in Daytona, Florida, hoping he would get more television coverage than at his rallies. He admitted he did not follow Nascar as closely as the most ardent fans. "But I have some friends who are Nascar owners," he said.

Polling firm Public Policy Polling puts Romney on 39% in Michigan, Santorum on 37%, Ron Paul on 19% and Newt Gingrich on 9%. In Arizona, where about half the electorate have already voted, the results so far are estimated to be two to one in Romney's favour.

National polls suggest that the intense infighting in a increasingly protracted Republican race is damaging the party, and that Barack Obama will be the main beneficiary. He will face the eventual winner of the Republican nomination race for the White House in November.

Santorum said that even to run Romney close in his home state was a victory of sorts. "This is not a place, frankly, that I thought we were going to be competing at the level we're competing," he said.

If Santorum were to win in Michigan it would give him momentum for the Super Tuesday contests next week. The most important is in Ohio, where a Quinnipiac poll on Monday showed Santorum on 36%, Romney on 29%, Gingrich on 17% and Paul on 11%.

To win the nomination a candidate needs 1,114 delegates, a majority of those attending the party convention in Tampa, Florida, in August. So far Romney has 123, Santorum 72, Gingrich 32 and Paul 19, according to an AP tally.

There are 29 delegates at stake in Arizona, a winner-takes-all contest, and 30 in Michigan, where the delegates will be distributed using roughly proportional representation. On Super Tuesday 419 delegates will be at stake.

Gingrich has not been campaigning in Michigan or Arizona, treating them as a lost cause, and is hoping to revive his campaign with wins on Super Tuesday in his home state, Georgia, and in Tennessee, which he toured on Monday.

Romney is the favourite to take Massachusetts, Vermont and Idaho, as well as Virginia, where Gingrich and Santorum, in organisational mix-ups, failed to get on the ballot.

Reflecting Santorum's growing importance, he is to receive secret service protection from Tuesday. Romney has had secret service protection since 1 February.

Gingrich has also requested protection. It is provided on the basis of importance as reflected in polls and also if specific threats have been made, as was the case with former Republican candidate Herman Cain who has since quit the race.